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I am a theoretical physicist working on the effects of topology and geometry in condensed matter physics. In particular, I am interested in packing problems, foams and the role played by conformal geometries in these systems.

Recent Publications

Columnar structures of soft spheres: metastability and hysteresis

A. Mughal, J. Winkelmann, D. Weaire and S. Hutzler, arXiv:1805.07673 (2018). Submitted to Phys. Rev. E.

Previously we reported on the stable (i.e. minimal enthalpy) structures of soft monodisperse spheres in a long cylindrical channel. Here, we present further simulations, which significantly extend the original phase diagram up to D/d = 2.714 (ratio of cylinder and sphere diameters), where the nature of densest sphere packing changes. However, macroscopic systems of this kind are not confined to the ideal equilibrium states of this diagram. Consequently, we explore some of the structural transitions to be expected as experimental conditions are varied; these are in general hysteretic. We represent these transitions in a stability diagram for a representative case. Illustrative videos are included in the supplemental material.


           Phase diagram for soft sphere packings in cylinders

Simulation and observation of line-slip structures in columnar structures of soft spheres

J. Winkelmann, B. Haffner, D. Weaire, A. Mughal and S. Hutzler, arXiv:1703.00773 (2017). Published in Phys. Rev. E.

We present the computed phase diagram of columnar structures of soft spheres under pressure, of which the main feature is the appearance and disappearance of line slips, the shearing of adjacent spirals, as pressure is increased. A comparable experimental observation is made on a column of bubbles under forced drainage, clearly exhibiting the expected line slip.


Observation of columnar structures of bubbles under forced drainage

How bees and foams respond to curved confinement: level set boundary representations in the Surface Evolver

 A. Mughal, T. Libertiny, G. E. Schroeder-Turk, arXiv:1611.10055 (2016). Published in Colloids & Surfaces A.

We present a Surface Evolver framework for simulating single bubbles and multicellular foams trapped between curved parallel surfaces. We are able to explore a range of geometries using level set constraints to model the bounding surfaces. Unlike previous work, in which the bounding surfaces are flat (the so called Hele-Shaw geometry), we consider surfaces with non- vanishing Gaussian curvature, specifically the sphere, the torus and the Schwarz Primitive-surface. In the case of multi-cellular foams - our method is to first distribute a set of N points evenly over the surface (using an en- ergy minimisation approach), these seed points are then used to generate a Voronoi partition, that is clipped to the confining space, which in turn forms the basis of a Surface Evolver simulation. In addition we describe our ex- perimental attempt to generate a honeycomb on a negatively curved surface, by trapping bees between two Schwarz Primitive-surfaces. Our aim is to understand how bees adapt the usual hexagonal motif of the honeycomb to cope with a curved surface. To our knowledge this is the first time that an attempt has been made to realise a biological cellular structure of this type.


              Attempt to build a bee honeycomb on a gyroid

© Adil Mughal 2012